Search existing math (mathlas index)

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description discloses the retrieval method (dense + BM25 + RRF fused with web findings) and optional corpus directory, adding significant behavioral context but not covering all constraints like rate limits or result filtering.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Two sentences efficiently cover purpose, method, usage, and parameters with no unnecessary words. Front-loaded with primary purpose.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Despite complexity (3 params, multiple retrieval methods), the description covers purpose, usage order, parameter details, and with an existing output schema, return values need no explanation. Complete for effective tool selection.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, and the description adds context beyond schema: clarifies query as 'problem/result description', notes default k=10, and explains corpus_dir as optional for parquets or prebuilt index.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the verb (find), resource (theorems/results from mathlas index), and purpose (solving 'does known math solve this?'), distinguishing it from siblings like search_formal_math.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicitly states 'Use FIRST for any 'does known math solve this?' question' and recommends follow-up with 'applicability_checklist', providing clear when-to-use and subsequent steps.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.